Question

The r.m.s current of an alternating current given by $i = 4\sqrt{2}\sin \omega t + 3\sqrt{2}\cos \omega t$ is:

• A. $5A$
• B. $3A$
• C. $5\sqrt{2}A$
• D. $2.5A$
• E. $7\sqrt{2}A$

Hint:

Combine sine and cosine using $\sqrt{a^2 + b^2}$.

Answer 1

The Correct Option is A

Concept:
• For: \[ i = a\sin\omega t + b\cos\omega t \] \[ i_{rms} = \frac{\sqrt{a^2 + b^2}}{\sqrt{2}} \]

Step 1: Identify
\[ a = 4\sqrt{2}, \quad b = 3\sqrt{2} \]

Step 2: Compute
\[ i_{rms} = \frac{\sqrt{(4\sqrt{2})^2 + (3\sqrt{2})^2}}{\sqrt{2}} \] \[ = \frac{\sqrt{32 + 18}}{\sqrt{2}} = \frac{\sqrt{50}}{\sqrt{2}} = \sqrt{25} = 5A \] Final Conclusion:
Option (A)